Ji-Cai Liu

activity

20142023

q

-binomial coefficients

105 citations · 168 across the 35 of their papers we have counts for

collaborators

Showing 2015Show all

2 papers · 1 filter

math.NT2015

Proof of a congruence on sums of powers of $q$ -binomial coefficients

Victor J. W. Guo, Ji-Cai Liu

We prove that, if $m, n ⩾ 1$ and $a_{1}, \dots, a_{m}$ are nonnegative integers, then \begin{align*} \frac{[a_1+\cdots+a_m+1]!}{[a_1]!\ldots[a_m]!}\sum^{n-1}_{h=0}q^h\prod_{i=1}^m…

math.NT2015

Proof of a conjecture of Z.-W. Sun on the divisibility of a triple sum

Victor J. W. Guo, Ji-Cai Liu

The numbers $R_{n}$ and $W_{n}$ are defined as \begin{align*} R_n=\sum_{k=0}^{n}{n+k\choose 2k}{2k\choose k}\frac{1}{2k-1},\ \text{and}\ W_n=\sum_{k=0}^{n}{n+k\choose 2k}{2k\choose k}\…

Proof of a congruence on sums of powers of q-binomial coefficients

Proof of a conjecture of Z.-W. Sun on the divisibility of a triple sum

Proof of a congruence on sums of powers of $q$ -binomial coefficients